Prime Minister Brian Mulroney was scrambling Wednesday to find ways of keeping Canada from breaking up over a prolonged constitutional deadlock hinging largely on the future status of French-speaking Quebec province.

Financial markets and political circles were in shock after Lucien Bouchard, the federal environment minister, abruptly resigned Tuesday, declaring that sovereignty association constituted the only option for Quebec."This country doesn't work any more; we have to remake it," Mr. Bouchard said.

Well known for his nationalist feelings about Quebec, Mr. Bouchard became the third member of parliament of the ruling Progressive Conservative Party within a week to bolt the Tory caucus.

After consulting Wednesday with Lowell Murray, the federal-provincial relations minister, the beleaguered Mr. Mulroney was to decide whether to convoke a special emergency meeting with all 10 provincial premiers.

On Wednesday, the Canadian dollar firmed up slightly to 84.36 U.S. cents in early morning trading, following a rough ride on Tuesday.

When it fell by more than one U.S. cent to 83.79 cents on Tuesday, the central bank intervened heavily, spending what one trader estimated at C$600 million to prop up the currency.

At the same time, interest rates rose sharply on the Canadian bond and money markets.

The Business Council on National Issues, which represents Canada's blue- chip companies, urged the political leaders to move quickly to avoid a crisis of confidence in the Canadian economy.

In recent months, Canada has been wracked by internal tensions between the French andEnglish-speaking communities as the deadline approaches for ratification of the so-called Meech Lake constitutional accord.

That accord is a package of constitutional amendments that would, among other things, recognize Quebec as a "distinct society" by virtue of its French heritage. In return, Quebec would join the constitution.

Scores of towns in Ontario declared themselves "unilingual," thereby

weakening the federal policy in favor of bilingualism and biculturalism. These actions were sparked, in part, by a Quebec law which permitted only French in outdoor commercial signs.

A key clause in the Meech Lake accord recognizes Quebec as a 'distinct society' within the Canadian confederation.

The pact must be ratified by all 10 provinces by June 23 or it will expire. Manitoba and New Brunswick have not approved it, while Newfoundland has rescinded its approval.

Premier Bourassa of Quebec, who approved the accord on the basis of five ''minimal" demands, said Quebecers have felt "betrayed" by other parts of Canada and he refuses to consider any amendments.

Mr. Bouchard's resignation was prompted by a package of recommendations by a parliamentary committee aimed at salvaging the Meech Lake agreement. He described them as a "booby trap."

A poll released earlier this week suggested that growing impatience with the Meech Lake impasse is driving a large number of Quebecers into the separatist camp.

The poll indicated that the proportion of Quebecers who prefer to live in an independent Quebec has increased to 41 percent from 32 percent in November. A majority of 54 percent still say they would rather remain part of Canada, but that is 10 percentage points less than six months ago.

In recent months, top Quebec businessmen, led by Claude Castonguay, chairman of the powerful Montreal-based Laurentian financial services group, have been sounding the alarm that a divorce from Canada would be costly for Quebec. But Quebec business opinion is nevertheless divided, with some top executives expressing belief that a separate Quebec is viable.